FSharp.Stats

FSharp.Stats is a multipurpose project for statistical testing, linear algebra, machine learning, fitting and signal processing.

Installation

From Nuget.org:

You can get all FSharp.Stats packages from nuget at https://www.nuget.org/packages/FSharp.Stats/.

To build the binaries yourself:

Windows:

• Install .Net Core SDK
• navigate to project folder
• use the console command ./build.cmd

Linux(Ubuntu, using Mono):

• Install .Net Core SDK
• navigate to project folder
• make the script executable with chmod +x ./build.sh
• use the console command ./build.sh

Example

The following examples show how easy it is to start working with FSharp.Stats.

Distributions

open FSharp.Stats

// initialize a normal distribution with mean 25 and standard deviation 0.1
let normalDistribution = Distributions.Continuous.normal 25. 0.1

// draw independently 30 times from the given distribution 
let sample = Array.init 30 (fun _ -> normalDistribution.Sample())

[|25.01546996; 25.0085751; 24.98655087; 24.97754422; 25.06064294; 25.12730136;
  25.15369078; 25.16191506; 25.09960277; 24.9804254; 24.84672728; 24.98691456;
  24.97149665; 24.86228433; 24.88944442; 25.07089216; 24.98596124; 25.03055411;
  25.05189345; 25.15010645; 24.98942086; 25.12237777; 24.78971587; 25.04044524;
  25.06452394; 25.02869547; 24.94641875; 24.78399431; 24.75855518; 24.9933029|]

Basic descriptive statistics

// calculate the mean of the given sample
let mean = Seq.mean sample

24.99784811

// calculate the bessel corrected sample standard deviation of the given sample
let stDev = Seq.stDev sample

0.1085530457

// calculate the coefficient of variation of the given sample 
// Attention: CV is valid only if a hypothetical real zero value exists for the data.
let cv = Seq.cv sample

0.004342495609

Vectors, Matrices and linear algebra

// create a vector 
let vecB = vector [19.;11.;35.]

// create a matrix 
let matA = matrix [[3.;4.;0.];[1.;2.;2.];[5.;0.;5.]]

// solve the linear system of equations
let vecX = FSharp.Stats.Algebra.LinearAlgebra.SolveLinearSystem matA vecB

vector [|5.0; 1.0; 2.0|]

Interpolation

let xData = vector [|1. .. 10.|]
let yData = vector [|4.;7.;9.;12.;15.;17.;16.;23.;5.;30.|]

// get coefficients of interpolating polynomial
let interpolatingCoefficients = 
    Interpolation.Polynomial.coefficients xData yData

// get fitting function of interpolating polynomial
let interpolFitFunc = 
    Interpolation.Polynomial.fit interpolatingCoefficients

Regression

// get coefficients of 3rd order regression polynomial
let regressionCoefficients = 
    Fitting.LinearRegression.OrdinaryLeastSquares.Polynomial.coefficient 3 xData yData
    
// get fitting function of 3rd order regression polynomial
let regressionFitFunc = 
    Fitting.LinearRegression.OrdinaryLeastSquares.Polynomial.fit 3 regressionCoefficients

The resulting interpolating and regression polynomials are plotted below using Plotly.NET.

Samples & documentation

The library comes with comprehensible documentation. It can include tutorials automatically generated from *.fsx files in the content folder. The API reference is automatically generated from Markdown comments in the library implementation.

• API Reference contains automatically generated documentation for all types, modules and functions in the library. This includes additional brief samples on using most of the functions.

Contributing and copyright

The project is hosted on GitHub where you can report issues, fork the project and submit pull requests. If you're adding a new public API, please also consider adding samples that can be turned into a documentation. You might also want to read the library design notes to understand how it works.

The library is available under Public Domain license, which allows modification and redistribution for both commercial and non-commercial purposes. For more information see the License file in the GitHub repository.